Transformations
Muhtasari
Every animated logo, every character walking across a game screen and every CAD drawing rotated on an engineer's monitor relies on the same four moves: reflect, rotate, translate, enlarge. Each one changes a shape's position or size in a precisely defined way, and each one can be described completely, without a picture, using nothing more than a few coordinates and numbers.
This topic builds fluency in all four transformations, including enlargements with negative and fractional scale factors, shows how two transformations combine into one, and introduces the 2x2 matrix as a compact way of carrying out (and identifying) a transformation algebraically.
Malengo
- Understand and use transformations of the plane including reflections in any line, rotations about any point, translations and enlargements
- Find and use combination of transformations
- Multiply a vector by a matrix to find the matrix for a given transformation of the plane
Ramani ya mawazo
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Kadi za kumbukumbu
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Maelezo ya Somo
Dokezo Kamili la Somo Linapatikana kwenye Programu ya Green Bridge
Pata programu ya Green Bridge CBT kwenye simu au kompyuta yako kwa maktaba kamili ya IGCSE: mitihani ya miaka iliyopita, miongozo ya usahihishaji, ramani za mawazo, kadi za marudio na masomo ya sauti.
Tathmini ya Somo
Hongera kwa kukamilisha somo la Transformations. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- Which transformation does NOT preserve the size of a shape? A) Reflection B) Rotation C) Translation D) Enlargement Answer: D
- A point (4, -1) is rotated 180 degrees about the origin. What is its image? A) (4, 1) B) (-4, 1) C) (-4, -1) D) (1, -4) Answer: B
- Which of these fully describes a translation? A) The distance moved only B) The column vector C) The angle and direction D) The scale factor and centre Answer: B
- An enlargement has scale factor -3. Compared with the object, the image is: A) 3 times the size, same side of the centre B) 3 times the size, opposite side of the centre C) 1/3 the size, same side of the centre D) the same size, rotated 180 degrees Answer: B
- What single transformation does the matrix (1 0; 0 -1) represent? A) Reflection in the y-axis B) Reflection in the x-axis C) Rotation of 180 degrees about the origin D) Enlargement, scale factor -1 Answer: B
Fanyia kazi maswali haya kwenye programu
Fanyia kazi maswali haya kwenye programu
Vitabu Vinavyopendekezwa
Fanya Mazoezi ya Maswali ya Majaribio
Ungependa kufanya mazoezi ya maswali ya majaribio kuhusu Transformations? Pakua programu ya Green Bridge CBT ili kupata maswali ya majaribio na tathmini kamili za mazoezi kuhusu mada hii.
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